Problem Statement

You are given strings S and T consisting of lowercase English letters and ?. Here, $|S| \gt |T| holds ($for a string X, |X| denotes the length of X).
Two strings X and Y such that |X|=|Y| is said to match if and only if:

• one can make X equal Y by replacing each ? in X and Y with any English letter independently.

Solve the following problem for each $x=0,1,\ldots,|T|$:

• Let S' be the string of length |T| obtained by concatenating the first x characters and the last (|T|-x) characters of S without changing the order. Print Yes if S' and T match, and No otherwise.

Input

The input is given from Standard Input in the following format:
S
T

Output

Print (|T|+1) lines.
The i-th line should contain the answer for x=i-1.

Constraints

• S and T are strings consisting of lowercase English letters and ?.
• $1 \leq |T| \lt |S| \leq 3 \times 10^5$

Sample Input 1

a?c
b?

Sample Output 1

Yes
No
No

When x=0, S' equals ?c. Here, we can replace the 1-st character of S', ?, with b and the 2-nd character of T, ?, with c to make S' equal T, so S' and T match. Thus, Yes should be printed in the first line.
When x=1 and 2, respectively, S' is ac and a?, neither of which matches with T. Thus, No should be printed in the second and third lines.

Sample Input 2

atcoder
?????

Sample Output 2

Yes
Yes
Yes
Yes
Yes
Yes

Sample Input 3

beginner
contest

Sample Output 3

No
No
No
No
No
No
No
No

见题面 Input 部分

见题面 Output 部分